Trump has nominated Judy Shelton for the Fed's Board of Governors, a position with significant influence over interest rate policy and the regulation of banks and financial markets.
Shelton has also expressed seemingly contradictory views on interest rate policy and once suggested that the federal government need not guarantee bank deposits.
In the aftermath of the Great Recession, when the unemployment rate peaked at 10% in 2009, Shelton opposed the Fed's ultra-low interest rate policy.
Besides Shelton, Trump has nominated Christopher Waller, director of research at the St. Louis Federal Reserve Bank, for a second vacancy on the seven-member Fed board.
And if she were to disagree with most of the other Fed policymakers, that could make it harder to interpret the Fed's policy direction.